# kaal:claim:6655138-026

**Claim.** Each surface must carry a per-agent rate limit enforced by stake escalation, since rate limits secure compactness of the action profile space and prevent generation explosions that would violate convexity, and reflection-surface rate limits must be tighter than per-surface rate limits to prevent reflection cascades.

**Type.** condition  **Support.** argued

**Holds when.**

- conditions for fixed-point existence and convergence

**Source quote.**

> Each surface Σ has a per-agent rate limit enforced by stake escalation, ensuring compactness of the action profile space. Rate limits prevent generation explosions that would violate convexity. Σ_R rate limits are tighter than per-surface rate limits to prevent reflection cascades.

**From.** Wulf A. Kaal, *Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems* (2026), VII.D Architectural conditions for fixed-point existence, AC1, page 20

**Cite as.** Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138

**Verify.** sha256 of source PDF `52cb210167f06f0c7a2581214b156326216543de80b8394320b629c045c9e214` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202026%20-%20Possibility%20Loops%20An%20Operational%20Architecture%20for%20Computative%20Economics%20in%20Agent%20Coordination%20Systems.pdf

**Topics.** institutional-design

**Keywords.** ac1, rate-limits, stake-escalation, convexity, fixed-point

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